Question

Check that the ratio ke2 /G memp is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

Solution
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The given ratio is ke2Gmcmp

Where,

G= Gravitational constant

Its unit is Nm2kg2.

me and mp= Masses of electron and proton.

Their unit is kg.

e= Electric charge.

Its unit is C.

k=A constant

=14π0

0= Permittivity of free space

Its unit is Nm2C2.

Unit of the given ratio ke2Gmcmp=[Nm2C2][C2][Nm2kg2][kg][kg]

=M0L0T0

Hence, the given ratio is dimensionless.

e=1.6×1019C

G=6.67×1011Nm2kg2

me=9.1×10631kg

mp=1.66×1027kg

ke2Gmcmp=9×109×(1.6×1019)26.67×1011×9.1×103×1.67×10222.3×1039

This is the ratio of electric force to the gravitational force between a proton and an electron, keeping distance between them constant.

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